I don't believe the Boeing Model 363 was the entry for the eventual B-36 contract. The Consolidated entries for this competition were initially chosen by the Materiel Division as the most promising in early October, 1941, the initial request for proposals having gone out to manufacturers in April of the same year, with the contract being let to Consolidated for their six-engine version on November 15, 1941.
The Model 363 does not appear to have been submitted to the Air Corps for consideration until that same November 15 date, based upon copies of the original 3-view and a number of original documents I have. The Model 363 (and a number of additional designs) seems to have been one of quite a number of design studies done by Boeing under Contract AC-19441. Essentially, these were "What will be build after the B-36?" in nature.
At this year's IPMS Nationals in Columbia, SC I shall be giving a presentation about Boeing's Unknown Heavy Bomber Designs of WWII and will go into detail about the Model 363 and over two dozen OTHER designs Boeing did at the time. The talk will be "image-heavy" as I have a TON of drawings and a lot of data.
Hope to see you there!
AlanG